24 ideas
| 1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
| Full Idea: Thales was the first thinker in the west to believe that the arché (the basis of things) was intelligible. | |
| From: comment on Thales (fragments/reports [c.585 BCE]) by David Roochnik - The Tragedy of Reason p.138 |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5 | |
| A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems. |
| 12463 | Unlike correspondence, truthmaking can be one truth to many truthmakers, or vice versa [Jacobs] |
| Full Idea: I assume a form of truthmaking theory, ..which is a many-many relation, unlike, say correspondence, so that one entity can make multiple truths true and one truth can have multiple truthmakers. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §1) | |
| A reaction: This sounds like common sense, once you think about it. One tree makes many things true, and one statement about trees is made true by many trees. |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete. | |
| From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1 | |
| A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed. |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2 | |
| A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert. |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt. |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality. |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6 | |
| A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it. |
| 14375 | If structures result from intrinsic natures of properties, the 'relations' between them can drop out [Jacobs] |
| Full Idea: If a relation holds between two properties as a result of their intrinsic natures, then it appears the relation between the properties is not needed to do the structuring of reality; the properties themselves suffice to fix the structure. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.1) | |
| A reaction: [the first bit quotes Jubien 2007] He cites a group of scientific essentialists as spokesmen for this view. Sounds right to me. No on seems able to pin down what a relation is - which may be because there is no such entity. |
| 14378 | Science aims at identifying the structure and nature of the powers that exist [Jacobs] |
| Full Idea: Scientific practice seems aimed precisely at identifying the structure and nature of the powers that exist. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.3) | |
| A reaction: Good. Friends of powers should look at this nice paper by Jacobs. There is a good degree of support for this view from pronouncements of modern scientists. If scientists don't support it, they should. Otherwise they are trapped in the superficial. |
| 12467 | Powers come from concrete particulars, not from the laws of nature [Jacobs] |
| Full Idea: The source of powers is not the laws of nature; it is the powerful nature of the ordinary properties of concrete particulars. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.2) | |
| A reaction: This pithily summarises my own view. People who think the powers of the world derive from the laws either have an implicit religious framework, or they are giving no thought at all to the ontological status of the laws. |
| 14377 | Possibilities are manifestations of some power, and impossibilies rest on no powers [Jacobs] |
| Full Idea: To be possible is just to be one of the many manifestations of some power, and to be impossible is to be a manifestation of no power. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.2.1) | |
| A reaction: [This remark occurs in a discussion of theistic Aristotelianism] I like this. If we say that something is possible, the correct question is to ask what power could bring it about. |
| 14376 | States of affairs are only possible if some substance could initiate a causal chain to get there [Jacobs] |
| Full Idea: A non-actual state of affairs in possible if there actually was a substance capable of initiating a causal chain, perhaps non-deterministic, that could lead to the state of affairs that we claim is possible. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.2) | |
| A reaction: [He is quoting A.R. Pruss 2002] That seems exactly right. Of course the initial substance(s) might create a further substance, such as a transuranic element, which then produces the state of affairs. I favour this strongly actualist view. |
| 14379 | Counterfactuals invite us to consider the powers picked out by the antecedent [Jacobs] |
| Full Idea: A counterfactual is an invitation to consider what the properties picked out by the antecedent are powers for (where Lewis 1973 took it to be an invitation to consider what goes on in a selected possible world). | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.4.3) | |
| A reaction: A beautifully simple proposal from Jacobs, with which I agree. This seems to be an expansion of the Ramsey test for conditionals, where you consider the antecedent being true, and see what follows. What, we ask Ramsey, would make it follow? |
| 14372 | Possible worlds are just not suitable truthmakers for modality [Jacobs] |
| Full Idea: Possible worlds are just not the sorts of things that could ground modality; they are not suitable truthmakers. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §3) | |
| A reaction: Are possible world theorists actually claiming that the worlds 'ground' modality? Maybe Lewis is, since all those concrete worlds had better do some hard work, but for the ersatzist they just provide a kind of formal semantics, leaving ontology to others. |
| 3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
| Full Idea: Necessity is the strongest of things, for it rules everything. | |
| From: report of Thales (fragments/reports [c.585 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.2.9 |
| 12466 | All modality is in the properties and relations of the actual world [Jacobs] |
| Full Idea: Properties and the relations between them introduce modal connections in the actual world. ..This is a strong form of actualism, since all of modality is part of the fundamental fabric of the actual world. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4) | |
| A reaction: This is the view of modality which I find most congenial, with the notion of 'powers' giving us the conceptual framework on which to build an account. |
| 14371 | We can base counterfactuals on powers, not possible worlds, and hence define necessity [Jacobs] |
| Full Idea: Together with a definition of possibility and necessity in terms of counterfactuals, the powers semantics of counterfactuals generates a semantics for modality that appeals to causal powers and not possible worlds. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §1) | |
| A reaction: Wonderful. Just what the doctor ordered. The only caveat is that if we say that reality is built up from fundamental powers, then might those powers change their character without losing their identity (e.g. gravity getting weaker)? |
| 12465 | Concrete worlds, unlike fictions, at least offer evidence of how the actual world could be [Jacobs] |
| Full Idea: Lewis's concrete worlds give a better account of modality (than fictional worlds). When I learn that a man like me drives a truck, I gain evidence for the fact that I can drive a truck. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §3) | |
| A reaction: Cf. Idea 12464. Jacobs still rightly rejects this as an account of possibility, since the possibility that I might drive a truck must be rooted in me, not in some other person who drives a truck, even if that person is very like me. |
| 12464 | If some book described a possibe life for you, that isn't what makes such a life possible [Jacobs] |
| Full Idea: Suppose somewhere deep in the rain forest is a book that includes a story about you as a truck-driver. I doubt that you would be inclined the think that that story, that book, is the reason you could have been a truck driver. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §3) | |
| A reaction: This begins to look like a totally overwhelming and obvious reason why possible worlds (especially as stories) don't give a good metaphysical account of possibility. They provide a semantic structure for modal reasoning, but that is entirely different. |
| 12469 | Possible worlds semantics gives little insight into modality [Jacobs] |
| Full Idea: If we want our semantics for modality to give us insight into the truthmakers for modality, then possible worlds semantics is inadequate. | |
| From: Jonathan D. Jacobs (A Powers Theory of Modality [2010], §4.4) | |
| A reaction: [See the other ideas of Jacobs (and Jubien) for this] It is an interesting question whether a semantics for a logic is meant to give us insight into how things really are, or whether it just builds nice models. Satisfaction, or truth? |
| 1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
| Full Idea: Thales says water is the first principle (which is why he declared the earth is on water); perhaps he concluded this from seeing that all food is moist. | |
| From: report of Thales (fragments/reports [c.585 BCE], A12) by Aristotle - Metaphysics 983b12 |
| 1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
| Full Idea: Thales seems, from what is recorded of him, to have supposed that the soul is something productive of movement, if he really said that the magnet has soul because it produces movement in iron. | |
| From: report of Thales (fragments/reports [c.585 BCE]) by Aristotle - De Anima 405a20 |
| 1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |
| Full Idea: When asked whether a man who did wrong could escape the notice of the gods, Thales is said to have replied: 'No, not even if he thinks wrong.' | |
| From: report of Thales (fragments/reports [c.585 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.Th.9 |